Conventional power steering systems for automobiles reduce the effort required by the driver to turn the steering wheel during parking and during steering at low speed where unassisted manual effort is high. Such conventional power steering systems also furnish power assist at higher vehicle speeds where the unassisted manual effort is considerably lower. U.S. Pat. Application Ser. No. 069818, filed 6 July 1987 now U.S. Pat. No. 4,768,604 by William Schipper and assigned to the assignee of this invention, describes a bypass type variable effort power steering system wherein the high pressure side of the steering assist fluid motor is progressively bypassed to the low pressure side of the fluid motor as vehicle speed increases to reduce the power assist at higher speed. A bypass type variable effort power steering system according to this invention incorporates a valve which increases the level of power assist as a function of the rate of fluid flow in the steering system.